The following references provide brief description of the prior art:
[1] X. Zhou, “HW Efficient Carrier Recovery Algorithms for Single-Carrier QAM systems,” in SPPCOM'12, OSA, paper SpTu3A.1 (2012).
[2] N. Sigron, I. Tselniker, and M. Nazarathy, “Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD),” Opt. Express 20, 1981-2003 (2012).
[3] I. Tselniker, N. Sigron and M. Nazarathy “Joint phase noise and frequency offset estimation and mitigation for optically coherent QAM based on adaptive multi-symbol delay detection (MSDD),” Opt. Express 20, 10944-10962 (2012).
[4] Nobuhiko Kikuchi, Shinya Sasaki, Tetsuya Uda, “Improvement of tolerance to intra-channel non-linear effect of coherent higher-order multilevel signaling with digital delay detection,” in ECOC'12, We,3.C.1 (2012).
[5] S. Zhang, P.-yuen Kam, C. Yu, J. Chen, “Decision-aided carrier phase estimation for coherent optical communication,” JLT 28, 1597 (2010).
[6] X. Liu and M. Nazarathy, “Coherent, self-coherent, and differential detection systems,” Ch.1 in “Impact of Nonlinearities on Fiber Optic Communications, (ed Kumar), Springer (2011).
[7] T. Pfau, S. Hoffmann, and R. Noe, “HW-efficient coherent digital receiver concept with feedforward carrier recovery for QAM constellations,” J. Lightwave Technol. 27, 989-999, (2009).
[8] J. Volder, “The CORDIC trigonometric computing technique,” IRE Tran. Electronic Computers EC-8, 330-334 (1959).
[9] R. Andraka, “A survey of CORDIC algorithms for FPGA based computers,” ACM/SIGDA FPGA '98, 191-200, (1998).
[10] Y. Atzmon, M. Nazarathy, “Laser Phase Noise in Coherent and Differential Optical Transmission Revisited in the Polar Domain,” J. Lightwave Technol. 27, 19-29 (2009).
[11] T. Pfau, X. Liu, S. Chandrasekhar, “Optimization of 16-ary Quadrature Amplitude Modulation Constellations for Phase Noise Impaired Channels,” paper Tu.3.A.6, European Conf. Opt. Comm., ECOC'11 (2011).
[12] M. Taylor, “Phase Estimation Methods for Optical Coherent Detection Using Digital Signal Processing,” J. Lightwave Technol. 24 (2009).
[13] Q. Zhuge et al, “Linewidth tolerant low-complexity pilot-aided phase recovery for M-QAM using superscalar parallelization,” OFC' 12.
[14] K. Itoh, “Analysis of the phase unwrapping algorithm,” Applied Optics, 21, p. 2470 (1982)
[15] Gdeisat and Lilley, “One-Dimensional Phase Unwrapping Problem,” available on the Internet at http://www.ljmu.ac.uk/GERI/CEORG_Docs/OneDimensionalPhase Unwrapping_Final.pdf.
Carrier recovery (CR) and in particular carrier phase and frequency estimation continue to pose performance and computational challenges, especially for higher order transmission constellations, imminent for deployment in the next phase of coherent optical communication systems upgrades for long-haul, metro and access applications.
A plethora of CR methods has been investigated [1]. Among those, Multi-Symbol Delay Detection (MSDD) [2-6] (alternatively referred to as Multi-Symbol Phase Estimation (MSPE) [6] or Maximum likelihood (ML) phase estimation [5]) is gradually gaining recognition as capable of delivering superior performance-complexity tradeoffs. In the wireless transmission context where it originated, MSDD was proven optimal for detection in white noise. In the optical transmission context, MSDD copes well with the combination of ASE, laser and nonlinear phase noises (PN) [4]. For QPSK systems, MSDD [2] is free of cycle slips and provides 1-2 dB OSNR lead over Viterbi & Viterbi CR, whereas for 16-QAM transmission, MSDD performance [3] trails by just a fraction of a dB below the extremely complex Blind Phase Search (BPS) CR [7], considered as a “benchmark”. Numerous CR variants have recently been investigated based on two-staged processing using a coarse BPS first stage feeding a second CR stage realized by various methods [1]. Such CR systems claim substantial reductions of complexity vs. BPS at the expense of some performance degradation. To best of our knowledge, the MSDD CR method for 16-QAM [3] outperforms these other CR methods while still offering less complexity. However, there is still room for further complexity reduction of the MSDD CR sub-system.